Final answer:
To amount to $10,000 in 5 years, approximately $135.41 should be deposited at the end of each month with a 7.5% interest rate.
Step-by-step explanation:
To calculate the amount that should be deposited at the end of each month in an account paying 7.5%, we can use the formula for the future value of an ordinary annuity:
FV = P * [(1 + r)^n - 1] / r
Where:
- FV is the future value (in this case, $10,000)
- P is the monthly deposit
- r is the interest rate per period (7.5% / 12)
- n is the number of periods (5 years * 12 months)
Plugging in the values:
10000 = P * [(1 + (0.075/12))^(5*12) - 1] / (0.075/12)
Simplifying the equation will give us:
P ≈ $135.41
So, approximately $135.41 should be deposited at the end of each month.